Answer to Question #237493 in Differential Equations for James

Question #237493
Solve the differential equation by separation of variables.

(x^3 + 2)y = x(y^4 + 3)y’
1
Expert's answer
2021-09-15T02:57:10-0400

"({x^3} + 2)y = x\\left( {{y^4} + 3} \\right)y' \\Rightarrow ({x^3} + 2)y = x\\left( {{y^4} + 3} \\right)\\frac{{dy}}{{dx}} \\Rightarrow \\frac{{{x^3} + 2}}{x}dx = \\frac{{{y^4} + 3}}{y}dy \\Rightarrow \\left( {{y^3} + \\frac{3}{y}} \\right)dy = \\left( {{x^2} + \\frac{2}{x}} \\right)dx \\Rightarrow \\frac{{{y^4}}}{4} + 3\\ln |y| = \\frac{{{x^3}}}{3} + 2\\ln |x| + C"

Answer: "\\frac{{{y^4}}}{4} + 3\\ln |y| - \\frac{{{x^3}}}{3} - 2\\ln |x| = C"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS